Himalayan_Expedition_Deaths

Author

Jayjit Das

This dataset allows us to delve into feature engineering procedures, such as subsampling to address class imbalance (given the significantly higher number of survivors compared to fatalities) and imputing missing data, particularly for expedition members with incomplete information, such as age.

Goal: To predict the probability of an Himalayan expedition member surviving or dying

Code

library(tidyverse)
library(tidymodels)
library(skimr)
library(plotly)
library(knitr)

Exploratory data analysis

Loading and exploring the dataset

Code

members <- read_csv("https://raw.githubusercontent.com/rfordatascience/tidytuesday/master/data/2020/2020-09-22/members.csv")
skim(members)

Data summary
Name	members
Number of rows	76519
Number of columns	21
_______________________
Column type frequency:
character	10
logical	6
numeric	5
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	n_unique
expedition_id	0	1.00	9	9	10350
member_id	0	1.00	12	12	76518
peak_id	0	1.00	4	4	391
peak_name	15	1.00	4	25	390
season	0	1.00	6	7	5
sex	2	1.00	1	1	2
citizenship	10	1.00	2	23	212
expedition_role	21	1.00	4	25	524
death_cause	75413	0.01	3	27	12
injury_type	74807	0.02	3	27	11

Variable type: logical

skim_variable	complete_rate	mean	count
hired	1	0.21	FAL: 60788, TRU: 15731
success	1	0.38	FAL: 47320, TRU: 29199
solo	1	0.00	FAL: 76398, TRU: 121
oxygen_used	1	0.24	FAL: 58286, TRU: 18233
died	1	0.01	FAL: 75413, TRU: 1106
injured	1	0.02	FAL: 74806, TRU: 1713

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
year	0	1.00	2000.36	14.78	1905	1991	2004	2012	2019	▁▁▁▃▇
age	3497	0.95	37.33	10.40	7	29	36	44	85	▁▇▅▁▁
highpoint_metres	21833	0.71	7470.68	1040.06	3800	6700	7400	8400	8850	▁▁▆▃▇
death_height_metres	75451	0.01	6592.85	1308.19	400	5800	6600	7550	8830	▁▁▂▇▆
injury_height_metres	75510	0.01	7049.91	1214.24	400	6200	7100	8000	8880	▁▁▂▇▇

How has the rate of expedition success and member death changed over time?

Code

plot1 <- members %>%
  group_by(year = 10 * (year %/% 10)) %>%
  summarise(
    died = mean(died),
    success = mean(success)
  ) %>%
  pivot_longer(died:success, names_to = "outcome", values_to = "percent") %>%
  ggplot(aes(year, percent, color = outcome)) +
  geom_line(alpha = 0.7, size = 1.5) +
  scale_y_continuous(labels = scales::percent_format()) +
  labs(x = "year", y = "% of expedition members", color = NULL)

plotly::ggplotly(plot1)

Is there a relationship between the expedition member’s age and success of the expedition or death? We can use the same code but just switch out year for age.

Code

plot2 <- members %>%
  group_by(age = 10 * (age %/% 10)) %>%
  summarise(
    died = mean(died),
    success = mean(success)
  ) %>%
  pivot_longer(died:success, names_to = "outcome", values_to = "percent") %>%
  ggplot(aes(age, percent, color = outcome)) +
  geom_line(alpha = 0.7, size = 1.5) +
  scale_y_continuous(labels = scales::percent_format()) +
  labs(x = "age", y = "% of expedition members", color = NULL)

plotly::ggplotly(plot2)

Are people more likely to die on unsuccessful expeditions?

Code

members %>%
  count(success, died) %>%
  group_by(success) %>%
  mutate(percent = scales::percent(n / sum(n))) %>%
  kable(
    col.names = c("Expedition success", "Died", "Number of people", "% of people"),
    align = "llrr"
  )

Expedition success	Died	Number of people	% of people
FALSE	FALSE	46452	98%
FALSE	TRUE	868	2%
TRUE	FALSE	28961	99%
TRUE	TRUE	238	1%

We can use a similar approach to see how different the rates of death are on different peaks in the Himalayas.

Code

members %>%
  filter(!is.na(peak_name)) %>%
  mutate(peak_name = fct_lump(peak_name, prop = 0.05)) %>%
  count(peak_name, died) %>%
  group_by(peak_name) %>%
  mutate(percent = scales::percent(n / sum(n))) %>%
  kable(
    col.names = c("Peak", "Died", "Number of people", "% of people"),
    align = "llrr"
  )

Peak	Died	Number of people	% of people
Ama Dablam	FALSE	8374	100%
Ama Dablam	TRUE	32	0%
Cho Oyu	FALSE	8838	99%
Cho Oyu	TRUE	52	1%
Everest	FALSE	21507	99%
Everest	TRUE	306	1%
Manaslu	FALSE	4508	98%
Manaslu	TRUE	85	2%
Other	FALSE	32171	98%
Other	TRUE	631	2%

Let’s make one last exploratory plot and look at seasons. How much difference is there in survival across the four seasons?

Code

plot3 <- members %>%
  filter(season != "Unknown") %>%
  count(season, died) %>%
  group_by(season) %>%
  mutate(
    percent = n / sum(n),
    died = case_when(
      died ~ "Died",
      TRUE ~ "Did not die"
    )
  ) %>%
  ggplot(aes(season, percent, fill = season)) +
  geom_col(alpha = 0.8, position = "dodge", show.legend = FALSE) +
  scale_y_continuous(labels = scales::percent_format()) +
  facet_wrap(~died, scales = "free") +
  labs(x = NULL, y = "% of expedition members")

plotly::ggplotly(plot3)

Let’s now create the dataset that we’ll use for modeling by filtering on some of the variables and transforming some variables to a be factors. There are still lots of NA values for age but we are going to impute those.

Code

members_df <- members %>%
  filter(season != "Unknown", !is.na(sex), !is.na(citizenship)) %>%
  select(peak_id, year, season, sex, age, citizenship, hired, success, died) %>%
  mutate(died = case_when(
    died ~ "died",
    TRUE ~ "survived"
  )) %>%
  mutate_if(is.character, factor) %>%
  mutate_if(is.logical, as.integer)

members_df

# A tibble: 76,507 × 9
   peak_id  year season sex     age citizenship hired success died    
   <fct>   <dbl> <fct>  <fct> <dbl> <fct>       <int>   <int> <fct>   
 1 AMAD     1978 Autumn M        40 France          0       0 survived
 2 AMAD     1978 Autumn M        41 France          0       0 survived
 3 AMAD     1978 Autumn M        27 France          0       0 survived
 4 AMAD     1978 Autumn M        40 France          0       0 survived
 5 AMAD     1978 Autumn M        34 France          0       0 survived
 6 AMAD     1978 Autumn M        25 France          0       0 survived
 7 AMAD     1978 Autumn M        41 France          0       0 survived
 8 AMAD     1978 Autumn M        29 France          0       0 survived
 9 AMAD     1979 Spring M        35 USA             0       0 survived
10 AMAD     1979 Spring M        37 W Germany       0       1 survived
# ℹ 76,497 more rows

Building a model

We’ll split or spend our data to generate training and testing sets.

Code

set.seed(111)
members_split <- initial_split(members_df, strata = died)
members_train <- training(members_split)
members_test <- testing(members_split)

We use resampling to evaluate model performance. Getting those resampled sets ready.

Code

set.seed(111)
members_folds <- vfold_cv(members_train, strata = died)
members_folds

#  10-fold cross-validation using stratification 
# A tibble: 10 × 2
   splits               id    
   <list>               <chr> 
 1 <split [51642/5738]> Fold01
 2 <split [51642/5738]> Fold02
 3 <split [51642/5738]> Fold03
 4 <split [51642/5738]> Fold04
 5 <split [51642/5738]> Fold05
 6 <split [51642/5738]> Fold06
 7 <split [51642/5738]> Fold07
 8 <split [51642/5738]> Fold08
 9 <split [51642/5738]> Fold09
10 <split [51642/5738]> Fold10

Next we build a recipe for data preprocessing.

First, we must tell the recipe() what our model is going to be (using a formula here) and what our training data is.
Next, we impute the missing values for age using the median age in the training data set. There are more complex steps available for imputation, but we’ll stick with a straightforward option here.
Next, we use step_other() to collapse categorical levels for peak and citizenship. Before this step, there were hundreds of values in each variable.
After this, we can create indicator variables for the non-numeric, categorical values, except for the outcome died which we need to keep as a factor.
Finally, there are many more people who survived their expedition than who died (thankfully) so we will use step_smote() to balance the classes.

The object members_rec is a recipe that has not been trained on data yet (for example, which categorical levels should be collapsed has not been calculated).

Code

library(themis)

members_rec <- recipe(died ~ ., data = members_train) %>%
  step_impute_median(age) %>%
  step_other(peak_id, citizenship) %>%
  step_dummy(all_nominal(), -died) %>%
  step_smote(died)

members_rec

Comparing two different models: a logistic regression model and a random forest model.

Code

glm_spec <- logistic_reg() %>%
  set_engine("glm")

glm_spec

Logistic Regression Model Specification (classification)

Computational engine: glm

Code

rf_spec <- rand_forest(trees = 1000) %>%
  set_mode("classification") %>%
  set_engine("ranger")

rf_spec

Random Forest Model Specification (classification)

Main Arguments:
  trees = 1000

Computational engine: ranger

Putting together tidymodels workflow()

Code

members_wf <- workflow() %>%
  add_recipe(members_rec)

members_wf

══ Workflow ════════════════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: None

── Preprocessor ────────────────────────────────────────────────────────────────
4 Recipe Steps

• step_impute_median()
• step_other()
• step_dummy()
• step_smote()

Now we can add a model, and the fit to each of the resamples. First, we can fit the logistic regression model. Setting a non-default metric set so we can add sensitivity and specificity.

Code

members_metrics <- metric_set(roc_auc, accuracy, sensitivity, specificity)

glm_rs <- members_wf %>%
  add_model(glm_spec) %>%
  fit_resamples(
    resamples = members_folds,
    metrics = members_metrics,
    control = control_resamples(save_pred = TRUE)
  )

glm_rs

# Resampling results
# 10-fold cross-validation using stratification 
# A tibble: 10 × 5
   splits               id     .metrics         .notes           .predictions
   <list>               <chr>  <list>           <list>           <list>      
 1 <split [51642/5738]> Fold01 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 2 <split [51642/5738]> Fold02 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 3 <split [51642/5738]> Fold03 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 4 <split [51642/5738]> Fold04 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 5 <split [51642/5738]> Fold05 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 6 <split [51642/5738]> Fold06 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 7 <split [51642/5738]> Fold07 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 8 <split [51642/5738]> Fold08 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 9 <split [51642/5738]> Fold09 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
10 <split [51642/5738]> Fold10 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>

Now fitting the random forest model.

Code

rf_rs <- members_wf %>%
  add_model(rf_spec) %>%
  fit_resamples(
    resamples = members_folds,
    metrics = members_metrics,
    control = control_resamples(save_pred = TRUE)
  )

Code

rf_rs

# Resampling results
# 10-fold cross-validation using stratification 
# A tibble: 10 × 5
   splits               id     .metrics         .notes           .predictions
   <list>               <chr>  <list>           <list>           <list>      
 1 <split [51642/5738]> Fold01 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 2 <split [51642/5738]> Fold02 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 3 <split [51642/5738]> Fold03 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 4 <split [51642/5738]> Fold04 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 5 <split [51642/5738]> Fold05 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 6 <split [51642/5738]> Fold06 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 7 <split [51642/5738]> Fold07 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 8 <split [51642/5738]> Fold08 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
 9 <split [51642/5738]> Fold09 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>    
10 <split [51642/5738]> Fold10 <tibble [4 × 4]> <tibble [0 × 3]> <tibble>

We have fit each of our candidate models to our resampled training set!

Evaluating model

Let’s evaluate our models.

Code

collect_metrics(glm_rs)

# A tibble: 4 × 6
  .metric     .estimator  mean     n std_err .config             
  <chr>       <chr>      <dbl> <int>   <dbl> <chr>               
1 accuracy    binary     0.615    10 0.00264 Preprocessor1_Model1
2 roc_auc     binary     0.703    10 0.0117  Preprocessor1_Model1
3 sensitivity binary     0.684    10 0.0158  Preprocessor1_Model1
4 specificity binary     0.614    10 0.00267 Preprocessor1_Model1

Well, this is middling but at least mostly consistent for the positive and negative classes. The function collect_metrics() extracts and formats the .metrics column from resampling results like the ones we have here.

Code

collect_metrics(rf_rs)

# A tibble: 4 × 6
  .metric     .estimator  mean     n  std_err .config             
  <chr>       <chr>      <dbl> <int>    <dbl> <chr>               
1 accuracy    binary     0.974    10 0.000757 Preprocessor1_Model1
2 roc_auc     binary     0.756    10 0.0131   Preprocessor1_Model1
3 sensitivity binary     0.152    10 0.00992  Preprocessor1_Model1
4 specificity binary     0.986    10 0.000690 Preprocessor1_Model1

The accuracy is great but that sensitivity is really bad with respect to logistic regression. The random forest model has not learnt recognition of both classes properly, even with the oversampling strategy. Let’s dig deeper into how these models are doing to see this more. For example, how are they predicting the two classes?

Code

glm_rs %>%
  conf_mat_resampled()

# A tibble: 4 × 3
  Prediction Truth      Freq
  <fct>      <fct>     <dbl>
1 died       died       56  
2 died       survived 2182  
3 survived   died       25.9
4 survived   survived 3474.

Code

rf_rs %>%
  conf_mat_resampled()

# A tibble: 4 × 3
  Prediction Truth      Freq
  <fct>      <fct>     <dbl>
1 died       died       12.5
2 died       survived   80.3
3 survived   died       69.4
4 survived   survived 5576.

The random forest model is quite bad at identifying which expedition members died, while the logistic regression model does about the same for both classes.

Visualizing the ROC curve

Code

plot5 <- glm_rs %>%
  collect_predictions() %>%
  group_by(id) %>%
  roc_curve(died, .pred_died) %>%
  ggplot(aes(1 - specificity, sensitivity, color = id)) +
  geom_abline(lty = 2, color = "gray9 ", size = 1.5) +
  geom_path(show.legend = FALSE, alpha = 0.6, size = 1.2) +
  coord_equal()

plotly::ggplotly(plot5)

It is finally time for us to return to the testing set. Notice that we have not used the testing set yet during this whole analysis; to compare and assess models we used resamples of the training set. Let’s fit one more time to the training data and evaluate on the testing data using the function last_fit().

Code

members_final <- members_wf %>%
  add_model(glm_spec) %>%
  last_fit(members_split)

members_final

# Resampling results
# Manual resampling 
# A tibble: 1 × 6
  splits                id             .metrics .notes   .predictions .workflow 
  <list>                <chr>          <list>   <list>   <list>       <list>    
1 <split [57380/19127]> train/test sp… <tibble> <tibble> <tibble>     <workflow>

The metrics and predictions here are on the testing data.

Code

collect_metrics(members_final)

# A tibble: 2 × 4
  .metric  .estimator .estimate .config             
  <chr>    <chr>          <dbl> <chr>               
1 accuracy binary         0.615 Preprocessor1_Model1
2 roc_auc  binary         0.689 Preprocessor1_Model1

Confusion matrix

Code

collect_predictions(members_final) %>%
  conf_mat(died, .pred_class)

          Truth
Prediction  died survived
  died       191     7273
  survived    96    11567

Coefficients of predictors

The coefficients (which we can get out using tidy()) have been estimated using the training data. If we use exponentiate = TRUE, we have odds ratios.

Code

members_final %>%
  pull(.workflow) %>%
  pluck(1) %>%
  tidy(exponentiate = TRUE) %>%
  arrange(estimate) %>%
  kable(digits = 3)

term	estimate	std.error	statistic	p.value
(Intercept)	0.000	0.938	-53.347	0.000
peak_id_MANA	0.263	0.041	-32.916	0.000
peak_id_other	0.266	0.033	-40.502	0.000
peak_id_EVER	0.362	0.035	-29.227	0.000
sex_M	0.460	0.030	-25.612	0.000
hired	0.488	0.056	-12.923	0.000
citizenship_other	0.587	0.032	-16.847	0.000
citizenship_Japan	0.706	0.037	-9.309	0.000
citizenship_Nepal	0.875	0.063	-2.133	0.033
season_Winter	0.884	0.042	-2.940	0.003
season_Spring	0.951	0.016	-3.231	0.001
age	0.991	0.001	-12.958	0.000
year	1.027	0.000	55.770	0.000
peak_id_CHOY	1.101	0.041	2.339	0.019
citizenship_UK	1.773	0.045	12.780	0.000
citizenship_USA	1.815	0.044	13.604	0.000
success	2.184	0.016	48.953	0.000
season_Summer	3.689	0.080	16.289	0.000

Visualizing the result

Code

plot4 <- members_final %>%
  pull(.workflow) %>%
  pluck(1) %>%
  tidy() %>%
  filter(term != "(Intercept)") %>%
  ggplot(aes(estimate, fct_reorder(term, estimate))) +
  geom_vline(xintercept = 0, color = "gray7", lty = 2, size = 1.2) +
  geom_errorbar(aes(
    xmin = estimate - std.error,
    xmax = estimate + std.error
  ),
  width = .2, color = "gray7", alpha = 0.7
  ) +
  geom_point(size = 2, color = "darkcyan") +
  labs(y = NULL, x = "Coefficent from logistic regression")

plotly::ggplotly(plot4)

The features with coefficients on the positive side (like climbing in summer, being on a successful expedition, or being from the UK or US) are associated with surviving.
The features with coefficients on the negative side (like climbing specific peaks including Everest, being one of the hired members of a expedition, or being a man) are associated with dying.

We need to consider the interpretation of model coefficients in the context of our model’s moderate predictive accuracy. The model may not capture all the factors influencing expedition survival. Additionally, the results indicate a heightened risk for native Sherpa climbers hired as expedition members in Nepal, underscoring the dangers associated with this particular demographic group during mountain expeditions.